In commission-adjusted comparative trial S123-0, running Grand Martingale against Flat Betting for 152 hands of EZ High-Tie (high-tie) on 110 units documents 10.11u vs 1.63u in expected toll and 44.63% vs 6.96% ruin under a 75-unit pit limit. Because every 8-deck coup is statistically independent under EZ Baccarat 3-Card 7 Push (1.028% edge) (1.0284% edge), progression rules alter drawdown speed and table-cap collisions without changing per-hand expectation.
Reference 8-deck shoe for Stress Cell S123 (Grand Martingale vs Flat Betting, Two-Shoe High-Tie Stall under EZ Baccarat Dragon 7 Push). Big Road shows Banker (red) and Player (blue); derived roads track symmetry.
Column 2 has 2 beads. Column 1 has 2 beads. Same depth → red (=).
Common table reading watchout: Comparing the wrong columns. Compare Column 2, the one that just finished, with Column 1.
Column 3 has 2 beads. Column 1 has 2 beads. Same depth → red (=).
Common table reading watchout: Comparing the wrong columns. Compare Column 3, the one that just finished, with Column 1.
Column 4 has 2 beads. Column 1 has 2 beads. Same depth → red (=).
Common table reading watchout: Comparing the wrong columns. Compare Column 4, the one that just finished, with Column 1.
Stress cell S123 compares 1-3-7-15-31-63-127 against 1-1-1-1 constant unit over 152 hands.
Probability of exhausting the 110-unit bankroll under a 75-unit house bet limit.
Theoretical erosion under EZ Baccarat 3-Card 7 Push (1.028% edge) (1.0284% house edge) across 152 coups.
Deepest unit trough triggered by a 5-hand run inside the high-tie shoe profile.
Reflects 17.11% tie frequency (26 pushes) and 4.85u in vigorish friction.
Under EZ High-Tie (1.0284% effective edge), multi-coup stress run S123-1 over 152 hands and a 110-unit treasury audits a -47u drawdown (44.63% ruin) for Grand Martingale (2x+1) against -15u (6.96% ruin) for Flat 1-Unit Baseline inside a 75-unit cap.
In discrete-time comparative trial S123-2, running Grand Martingale against Flat Betting for 152 hands of EZ High-Tie (high-tie) on 110 units profiles 10.11u vs 1.63u in expected toll and 44.63% vs 6.96% ruin under a 75-unit pit limit.
| S123 ledger | Grand Martingale | Flat Betting |
|---|---|---|
| Grand Martingale / Flat Betting Rule | 1-3-7-15-31-63-127 | 1-1-1-1 constant unit |
| 152-Hand Ruin (110u) | 44.63% | 6.96% |
| EZ High-Tie Hold (1.0284%) | 10.11u | 1.63u |
| 5-Run Trough (75u Cap) | -47u | -15u |
Under EZ High-Tie (1.0284% effective edge), drawdown-weighted stress run S123-3 over 152 hands and a 110-unit treasury verifies a -47u drawdown (44.63% ruin) for Grand Martingale (2x+1) against -15u (6.96% ruin) for Flat 1-Unit Baseline inside a 75-unit cap.
In capital-bounded comparative trial S123-4, running Grand Martingale against Flat Betting for 152 hands of EZ High-Tie (high-tie) on 110 units benchmarks 10.11u vs 1.63u in expected toll and 44.63% vs 6.96% ruin under a 75-unit pit limit.
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Verify 8-deck combinatorial probabilities, Banker/Player house edge, and commission rules.
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